Download Standards for Mathematical Practice - MELT-Institute

Overview
Dr Kwaku Adu-Gyamfi
Stefanie Smith
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 Work
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with your group
Who did you work with?
What did you learn about them?
Their knowledge of mathematics
Their problem solving techniques
Their mathematical preferences?
 Present
your Solutions
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 Mathematics
involved in the task
 Pedagogy experienced
 Connecting task to CCSSM and the
mathematical Practices
 Adjusting the task for your class needs
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 Goal
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Identify the domains, clusters and concept
categories included in the standards
Identify and connect the standards for
mathematical practice to the National Council of
Teachers of Mathematics process standards
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 Aligned
with college and work expectations
 Maintains
focus on what matters most for
readiness
 Include
rigorous content and application of
knowledge through high-order skills
 Build
upon strengths and lessons of current
state standards
 Internationally
benchmarked so that all students
are prepared to succeed in our global economy
and society
 State
led
 Focus
•
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and coherence
Focus on key topics at each grade level.
Coherent progressions across grade levels.
 Balance
•
of concepts and skills
Content standards require both conceptual
understanding and procedural fluency.
 Mathematical
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Foster reasoning and sense-making in mathematics.
 College
•
practices
and career readiness
Level is ambitious but achievable.
What the Standards do NOT define
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How teachers should teach
All that can or should be taught
The nature of advanced work beyond the
core
The interventions needed for students well
below grade level
The full range of support for learners and
students with special needs
Everything needed to be college and
career ready
To be effective in improving education and getting all
students ready for college, workforce training, and
life, the Standards must be partnered with a contentrich curriculum and robust assessments, both aligned
to the Standards.

NC Curriculum
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MATH1 /MATH2
Algebra1/Algebra2
Integrated
NC Themes
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Algebra Theme
Geometry Theme
Functions Theme
Statistics Theme
STANDARDS FOR HIGH SCHOOL
MATHEMATICS
9-12
Part 1
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Standards for Mathematical Content

Defines what students should understand and be
able to do (conceptual categories)
Standards for Mathematical Practice
 Describes habits of mind of a mathematically
proficient student
CCSS= Math content + Math practices
 Organized

by conceptual categories
The big ideas that connect mathematics across
high school
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Number and Quantity
Algebra
Functions
Modeling
Geometry
Statistics and Probability
 Elaborated through domains, clusters and
standards
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Linear Algebra
 Calculus
 Abstract Algebra
 Introduction to proof
 Geometry
 Statistics and
Probability

College
Number and Quantity
 Algebra
 Functions
 Modeling
 Geometry
 Statistics and
Probability

High School
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Domain
Content
standard
Cluster
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Domains: are larger groups that progress across
grades (Big Idea)
Content standards: defines what students should
understand and be able to do with the big idea
(Objectives)
Clusters are groups of related standards (content
needed to be covered for the said objective)
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Clusters
Content
Domain
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 Work
with your partner (from the race track
activity)
 Go to the function section of the common
core (CCSSM) document
 Pick out a domain, identify the standards and
clusters associated with the domain
 Create a chart/visual or concept map that
helps address the connection between
Domain Content Clusters
 Color code your chart…
 Post your Chart Paper
 Gallery Walk…
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Part 2
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 Make
sense of problems and persevere in
solving them
 Reason abstractly and quantitatively
 Construct viable arguments and critique the
reasoning of others
 Model with mathematics
 Use appropriate tools strategically
 Attend to precision
 Look for and make use of structure
 Look for an express regularity in repeated
reasoning
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 Describes
varieties of expertise that
proficient mathematics students naturally
have
 Practices that all teachers should develop in
their students
 Practices rests on important processes and
proficiencies of importance in mathematics
education
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Process standards
Mathematical proficiency strands
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 Process
Standards
 Problem Solving
 Reasoning and
Proof
 Communication
 Connections
 Representations
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
Conceptual Understanding

Procedural Fluency

ability to formulate, represent and solve mathematical
problems
Adaptive Reasoning

skill in carrying out procedures flexibly, accurately,
efficiently and appropriately
Strategic Competence

comprehension of mathematical concepts, operations
and relations
capacity for logical thought, reflection, explanation and
justification
Productive disposition
inclination to see mathematics as sensible useful and
worthwhile, coupled with a belief in diligence and one’s
own efficacy
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 Take
a moment to examine the first three
words of each of the 8 mathematical
practices..what do you notice?
 What are the verbs that illustrate the
student actions for an identified
mathematical practice?
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
Circle, highlight or underline them for your
assigned practice
Discuss with a partner, what jumps out at you?
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 Stay
in the same groups as for the previous
activity
 Each group is assigned 1-3 mathematical
practices to review
 Each group construct tasks that reflect their
assigned practices
 Write tasks on chart paper
 Discuss challenges with regard to developing
tasks
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What I Know
about the
CCSSM
What I want to What I learned
Know about
about the
the CCSSM
CCSM
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A function or not a function activity
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Overview of Mathematics Task Types
PARCC mathematics assessments will include three types of tasks.
Task Type
Description of Task Type
I. Tasks assessing
concepts, skills and
procedures
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Balance of conceptual understanding, fluency, and application
Can involve any or all mathematical practice standards
Machine scorable including innovative, computer-based formats
Will appear on the End of Year and Performance Based Assessment
components
II. Tasks assessing
expressing
mathematical
reasoning
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Each task calls for written arguments / justifications, critique of
reasoning, or precision in mathematical statements (MP.3, 6).
Can involve other mathematical practice standards
May include a mix of machine scored and hand scored responses
Included on the Performance Based Assessment component
III. Tasks assessing
modeling /
applications
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•
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Each task calls for modeling/application in a real-world context or
scenario (MP.4)
Can involve other mathematical practice standards.
May include a mix of machine scored and hand scored responses
Included on the Performance Based Assessment component
For more information see PARCC Item Development ITN Appendix D.